In this example, we will solve this equation on the surface of a coil, which is generated by an helix with 30 mm of diameter and 12 mm per revolution of pitch. This curve is extruded with a circular cross-section with 5 mm of radius. The resulting geometry can be seen in Figure REF , which is discretized with 1546 points and 3044 triangles. We can generate a ground truth solution of the Eikonal equation by randomly selecting a point on the mesh for \(\mbox{$x$}{}_b\)  and then applying the exact geodesic algorithm [1]} as implemented in libigl [2]}. We randomly select 40 points of this solution to use as data \(u_i\) . In this case, the partial differential equation loss defined in REF  takes the form:
\(MSE_{\rm PDE}(\theta ) = \frac{1}{R}\sum _i^R \left(\sqrt{({\mbox{$B$}{}^e_r}\hat{\mbox{$u$}{}}^e_r) \cdot (\mbox{$B$}{}^e_r \hat{\mbox{$u$}{}}^e_r)}-1\right)^2\) 
